Functionally graded surface has been a domain of research interest due to its use in various technologically advanced applications. The work focuses on static and dynamic analysis of rough fractal surface with exponentially graded material properties. The rough fractal surface is modeled in ANSYS with the coordinate points generated using the two variable modified Weierstrass–Mandelbrot function. Material gradation is applied to the rough surface model in such a way that, for any value of the gradation or inhomogeneity parameter, material properties at the top of the rough surface always remain constant. Force–displacement behavior of the fractal surface in contact with a rigid flat surface is determined through finite element simulation. A parameter representing the nonlinearity of the system is extracted from the force–displacement plot. It is found that higher is the inhomogeneity parameter, higher is the nonlinearity of the system. Furthermore, for a certain change in inhomogeneity parameter, the change in nonlinearity is higher for rougher topography. The dynamic contact system is found to be softening in nature, and the softening nature increases with higher inhomogeneity parameter. The phase plot of the vibrating contact system becomes more asymmetric with respect to the velocity axis for higher value of inhomogeneity parameter.

中文翻译：

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功能梯度分形面的接触行为

由于其在各种技术先进的应用中的使用，功能梯度表面一直是一个研究兴趣领域。工作重点是对具有指数渐变材料特性的粗糙分形表面进行静态和动态分析。粗糙的分形表面在 ANSYS 中建模，坐标点使用两个变量修正的 Weierstrass-Mandelbrot 函数生成。材料渐变应用于粗糙表面模型的方式是，对于渐变或不均匀性参数的任何值，粗糙表面顶部的材料属性始终保持不变。分形表面与刚性平面接触的力-位移行为是通过有限元模拟确定的。从力-位移图中提取代表系统非线性的参数。发现不均匀性参数越高，系统的非线性度越高。此外，对于不均匀性参数的一定变化，对于更粗糙的地形，非线性变化更高。发现动态接触系统本质上是软化的，并且软化特性随着不均匀参数的增加而增加。对于更高的非均匀性参数值，振动接触系统的相位图相对于速度轴变得更加不对称。